CN113114318B - Novel millimeter wave multi-user beam alignment method - Google Patents

Novel millimeter wave multi-user beam alignment method Download PDF

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CN113114318B
CN113114318B CN202110416757.9A CN202110416757A CN113114318B CN 113114318 B CN113114318 B CN 113114318B CN 202110416757 A CN202110416757 A CN 202110416757A CN 113114318 B CN113114318 B CN 113114318B
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CN113114318A (en
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程龙
易志立
王志强
岳光荣
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0452—Multi-user MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0854—Joint weighting using error minimizing algorithms, e.g. minimum mean squared error [MMSE], "cross-correlation" or matrix inversion
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention belongs to the technical field of communication, and particularly relates to a beam alignment scheme based on a dilution coding theory in a millimeter wave multi-user scene. The invention firstly converts the uplink multi-user beam alignment problem into a dilution coding and decoding problem through the reasonable design of the transmitting beam and the receiving beam, and simultaneously decomposes the measurement matrix into two parts, namely a dilution coding matrix and a detection matrix. Then, a dilution detection matrix, and a detection method are proposed based on the received coding matrix of the dilution coding.

Description

Novel millimeter wave multi-user beam alignment method
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a wave beam alignment method based on a sparse coding theory in a millimeter wave multi-user scene.
Background
Driven by technologies such as ultra-high-definition video, intelligent vehicle-mounted communication and virtual reality, the capacity of a global mobile system will increase sharply in the coming years. Whereas millimeter wave technology may utilize greater communication bandwidth and rate for communication. However, transmission in the millimeter wave band has a higher path loss than that in the low frequency band. Whereas large-scale antenna arrays may compensate for energy attenuation of the signal by beamforming. Challenges are presented to the design of massive MIMO channel estimation algorithms operating in millimeter wave environments.
In recent years, we estimate the channel using methods based on CS or CP decomposition by exploiting the sparsity of the mmwave MIMO channel. However, these algorithms have high computational complexity due to the large matrix operation. To reduce computational complexity, the academia has studied a series of beam scanning and search algorithms. Clearly, the simplest and intuitive beam search method is to search all candidate beams exhaustively, but it has a high sampling complexity. To solve this problem, some literature adaptive algorithms propose a method for reducing pilot overhead based on a hierarchical beam scanning codebook, but require a feedback link. Specifically, some documents implement the cancellation of the feedback link by using Pseudo-Random Spreading Codes (PRSC), but it needs a Pseudo-Noise sequence (PN) sufficiently long to ensure the independence of different beams. Therefore, there is an urgent need to design a new millimeter wave beam alignment scheme to reduce pilot sequences while maintaining good performance.
Disclosure of Invention
The invention aims to design a novel beam alignment scheme based on a sparse coding theory to be applied to a millimeter wave multi-user scene. The invention firstly converts the uplink multi-user beam alignment problem into a dilution coding and decoding problem through the reasonable design of the transmitting beam and the receiving beam, and simultaneously decomposes the measurement matrix into two parts, namely a dilution coding matrix and a detection matrix. Then, a dilution detection matrix, and a detection method are proposed based on the received coding matrix of the dilution coding.
The core idea of the invention is to realize millimeter wave multi-user uplink beam alignment by using a dilution coding structure.
To effectively explain the algorithm structure to be studied in this section, first consider a typical mm-wave Multi-User Multiple Input Multiple Output (MU-MIMO) system, as shown in fig. 1, in which a Base Station (BS) communicates with K users simultaneously. Suppose that the BS side is equipped with NRA receiving antenna and NRFA radio frequency link (N)RF<NR) And the kth User (User, UE) is equipped with MTAn antenna and MRFA radio frequency link. In order to realize spatial multiplexing under the conditions of low complexity and low power consumption, a hybrid precoding architecture is used by the BS and the UE. Thus, the millimeter wave uplink multi-user channel of the transmitting and receiving end can be expressed as follows
Figure BDA0003026233140000021
Wherein
Figure BDA0003026233140000022
AOA, AOD, and channel complex gain of the ith path, respectively, representing the kth user. Also, due to the unique properties of the millimeter wave channel, the complex gain of the millimeter wave channel may be modeled as a rice fading profile as follows
Figure BDA0003026233140000023
Wherein
Figure BDA0003026233140000024
Integral complex gain amplitude of the channel, ηl,kRepresents the ratio of LOS path components to NLOS path components, and
Figure BDA0003026233140000025
representing a complex gaussian random variable. In addition, the ULA is used at the transceiving end, so that the vector is pointed to
Figure BDA0003026233140000026
And
Figure BDA0003026233140000027
are respectively represented as
Figure BDA0003026233140000028
Figure BDA0003026233140000029
Where λ denotes the wavelength, where d is set to λ/2.
Again for an abstract understanding of our algorithmic logic,we are illustrated in figure 2. The measurement matrix is sparse, non-zero beam indexes are estimated through the sparse measurement matrix, and a problem with sparsity of 3 is converted into a problem with sparsity of 1 and sparsity of 2 through the sparse measurement matrix. The invention has more involved concepts and simply lists and dilutes the coding matrix
Figure BDA00030262331400000210
The relationship with the actual transmit beam is shown in figure 3. Meanwhile, according to the multipath distribution of the millimeter wave channel and the degree distribution of the received pins, the following types can be defined
(1) And (4) zero pin: define a right node as zero pin when it is not connected to the virtual angle domain channel
Figure BDA0003026233140000031
Is a non-zero element of (c).
(2) Single pin: defining a right node as a single pin as it has and communicates only with the angular domain
Figure BDA0003026233140000032
One non-zero element is connected.
(3) Multiple pins: defining a right node as a multi-pin channel with angle domain
Figure BDA0003026233140000033
A plurality of non-zero elements are connected.
The invention provides a sparse coding-based beam alignment method, which comprises the following steps:
step 1, firstly, a BS end receives a plurality of UE transmitting beams simultaneously and passes through an RF integration matrix
Figure BDA0003026233140000034
And a digital integration matrix
Figure BDA0003026233140000035
The beamforming codebook is then customized locally, e.g. W (t) ═ WRF(t)WBB(t)＝FBSv (t), where v (t) represents an index matrix of quantization angles, where the non-zero values are 1, FBSRepresenting a DFT matrix. The BS side receives data by using different RF links, and the signal of the receiving side can be expressed as
Figure BDA0003026233140000036
Wherein
Figure BDA0003026233140000037
And K represents the RF precoding matrix, the digital precoding matrix and the number of the UE in the uplink channel respectively. N (t) to CN (0,1) represent additive noise vectors of Gaussian distribution.
The receiver processes each RF link individually at a time, and the data at the receiver is represented here for simplicity as
Figure BDA0003026233140000038
Wherein
Figure BDA0003026233140000039
Is a beam space representation method in which
Figure BDA00030262331400000310
And
Figure BDA00030262331400000311
to represent the DFT matrix, the DFT matrix is shown,
Figure BDA00030262331400000312
represents a virtual angular domain index, and
Figure BDA00030262331400000313
indicating selection
Figure BDA00030262331400000314
One line of (1), fkAnd (t) is a transmission vector of k users.For the BS side, the receive side beam space is periodically scanned by simultaneously forming multiple beams.
In the following description, we simplify riR for the following description.
Step 2, UE simultaneously transmits a plurality of wave beams, and the transmission vector is fk(t)＝FRF,k(t)FBB,k(t)＝FMSψk(t) in which
Figure BDA0003026233140000041
The coding matrix representing the kth user, based on the formula in step 1, can be expressed as
Figure BDA0003026233140000042
Wherein
Figure BDA0003026233140000043
Step 3, the data by collecting T time can be expressed as
Figure BDA0003026233140000044
Step 4, defining T ═ MN, and designing a measurement matrix
Figure BDA0003026233140000045
Divide it into two parts, wherein the sparse coding matrix
Figure BDA0003026233140000046
And a detection matrix
Figure BDA0003026233140000047
In this way, the measurement matrix ψ can be obtained
ψ＝G⊙S
Wherein |, indicates a line tensor operation. Mathematically, the measurement matrix psi can be re-expressed as
Figure BDA0003026233140000048
Wherein G isiAnd SiRespectively represent the ith columns of matrix G and matrix S, an
Figure BDA0003026233140000049
Representing the Kronecker product.
Step 5, constructing a sparse coding matrix
Figure BDA00030262331400000410
The bipartite graph whose design criteria derive from the use of the algorithm is a rule bipartite graph
Figure BDA00030262331400000411
Derived from the collection. In this set, the m-th detection node is divided into d stages, where each left node is randomly connected to one right node at each stage. Definition set F ═ { F1…fdRepresents the number of right nodes at the stage i as fi. And, for all i and random redundancy parameters μ, fiμ K + o (1). The parameters mu are selected and the corresponding layer number d is shown in the following table 1:
TABLE 1 parameter μ selection and corresponding layer number d
d 3 4 5 6 7 8
μ 1.221 1.292 1.425 1.566 1.715 1.864
The encoding matrix is then designed such that each phase possesses a cyclically shifted sub-sampling pattern. When the diluting coding matrix is specifically designed, the number of layers and the number of rows which meet the requirements of the bipartite graph are designed, then the non-zero values in each row are translated in a randomized circulation mode, and the non-zero values appear in each node in a circulation mode for sampling.
Step 6, aiming at the noise scene, designing a diluted detection matrix
Figure BDA0003026233140000051
The columns in which each stage has a value can be represented as
Figure BDA0003026233140000052
Wherein M isiIs the number of non-zero elements in the matrix G in each layer. In particular, to effectively combat the effects of noise, the matrix DiThe medium element is a random gaussian variable and remains constant modulo. In order to effectively explain the coding structure, as shown in fig. 4, the relationship between the measurement matrix and the sparse coding matrix is shown; and transmitting beams through the constructed sparse coding matrix and the sparse detection matrix.
Step 7, detecting whether the receiving vector is zero or not as follows
Figure BDA0003026233140000053
Wherein
Figure BDA0003026233140000054
Which is indicative of the minimum signal power,
Figure BDA0003026233140000055
is the minimum noise power, ε1Is zero pin detection threshold, ri,j[1]And correspondingly diluting the received first numerical value of the jth pin vector in the ith stage and the jth pin vector sent in the encoding matrix.
Step 8, if the received vector is not zero-pin, then the received pin vector is assumed to be single-pin and the beam index pair thereof is estimated at the same time
Figure BDA0003026233140000056
Specifically, for the ith pin of each layer, the most likely coefficient is obtained using a Maximum Likelihood (ML) algorithm as follows
Figure BDA0003026233140000057
Thus, estimated
Figure BDA0003026233140000058
Expressed as the minimum value of the following parameters
Figure BDA0003026233140000059
Step 9, using known checking steps to decide whether the received vector is a single pin, and the following decision criteria are used as follows
Figure BDA00030262331400000510
Wherein
Figure BDA00030262331400000511
Which is indicative of the minimum signal power,
Figure BDA00030262331400000512
is the minimum noise power, ε2Is a single pin detection threshold.
Step 10, if the received vector is detected to be a single pin, then
Figure BDA0003026233140000061
The process of multiple iteration can be artificially set for L times of iteration, and meanwhile, when a single pin of the UE user number is found, the iteration is stopped. Finally, the estimated mapping
Figure BDA0003026233140000062
To the actual beam index
Figure BDA0003026233140000063
The invention is mainly applied to a millimeter wave multi-antenna communication system, and has the advantages that:
1) compared with the traditional CS-based channel estimation algorithm, the proposed uplink multi-user estimation method has shorter operation calculation time and obtains similar performance to the traditional method under the condition of correspondingly improving the pilot frequency overhead.
2) Compared with the latest beam alignment algorithm, the detection probability under the same measurement overhead is improved by the algorithm.
Drawings
FIG. 1 is a schematic diagram of a millimeter wave Massive MIMO communication system according to the present invention;
FIG. 2 is a logic diagram of millimeter wave diluting encoding beam alignment algorithm in the algorithm
FIG. 3 is a schematic diagram of the relationship between the sparse coding matrix and the transmit beam in the present invention;
fig. 4 is a regular bipartite graph corresponding to a sparse coding matrix in the present invention, where the right degree is b-2;
FIG. 5 shows that the detection probability of the proposed algorithm and the latest random search algorithm under different measurement overheads in a noisy sceneBy contrast, where SNR is 5dB, and N of the random search algorithmc＝32。
Fig. 6 shows the comparison between the proposed algorithm and the distribution lattice point matching algorithm under different SNR conditions in the noise scene and under the alignment condition according to the present invention, and the measurement overhead of the two algorithms is 256 and 96 respectively.
Detailed Description
The technical scheme of the invention is described in detail in the following by combining the attached drawings and examples.
Examples
In this example, the number of users is set to K16, the BS terminal uses a unit line array, and N is the numberR64 and NRFThe UE uses a unit line array, M, 16T16 and M RF4. Meanwhile, assume that the number of multipaths of different users is L k4 and K factor in the channel is Kfactor＝20dB。
The example includes the following steps
Step 1: the BS end utilizes a plurality of RF links to simultaneously form a plurality of beams, the receiving end traverses and searches each possible path at each sending moment, and simultaneously the receiving end separates data received by different beams to be respectively processed.
Step 2: transmitting end constructing sparse coding matrix
Figure BDA0003026233140000071
The bipartite graph whose design criteria derive from the use of the algorithm is a rule bipartite graph
Figure BDA0003026233140000072
Derived from the collection. In this set, the m-th detection node is divided into d stages, where each left node is randomly connected to one right node at each stage. We define the set F ═ { F1…fdRepresents the number of right nodes at the stage i as fi. And, for all i and random redundancy parameters μ, fiμ K + o (1). Wherein the parameters μ are selected and the corresponding number of layers d is shown in Table 1 below
TABLE 1 parameter μ selection and corresponding layer number d
d 3 4 5 6 7 8
μ 1.221 1.292 1.425 1.566 1.715 1.864
The coding matrix is then designed based on the bipartite graph so that each phase has a cyclically shifted sub-sampling pattern.
And step 3: multiple user transmitting end joint transmitting beam, its joint dilution coding matrix
Figure BDA0003026233140000073
Constructing a sparse detection matrix, wherein a diluted detection matrix is designed
Figure BDA0003026233140000074
The columns in which each stage has a value can be represented as
Figure BDA0003026233140000075
Wherein M isiIs the number of non-zero elements in the matrix G in each layer. In particular, to effectively combat the effects of noise, the matrix DiThe medium element is a random gaussian variable and remains constant modulo. In order to effectively explain the coding structure, as shown in fig. 3, the relationship between the measurement matrix and the sparse coding matrix is shown.
And 4, step 4: the beam is transmitted one by one according to logic similar to that in figure 3 through the constructed sparse coding matrix and the sparse detection matrix.
And 5: the detection of whether the received vector is zero or not is as follows
Figure BDA0003026233140000076
Wherein
Figure BDA0003026233140000077
Which is indicative of the minimum signal power,
Figure BDA0003026233140000078
is the minimum noise power, ε1Is zero pin detection threshold, ri,j[1]And correspondingly diluting the received first numerical value of the jth pin vector in the ith stage and the jth pin vector sent in the encoding matrix.
Step 6: if the received vector is not a zero-pin, then the received pin vector is assumed to be a single pin while estimating its beam index pair
Figure BDA0003026233140000081
Specifically, for the ith pin of each layer, the most likely coefficient is obtained using a Maximum Likelihood (ML) algorithm as follows
Figure BDA0003026233140000082
Thus, estimated
Figure BDA0003026233140000083
Expressed as the minimum value of the following parameters
Figure BDA0003026233140000084
And 7: the decision whether a received vector is a single-pin is determined using known checking steps, with the following decision criteria
Figure BDA0003026233140000085
Wherein
Figure BDA0003026233140000086
Which is indicative of the minimum signal power,
Figure BDA0003026233140000087
is the minimum noise power, ε2Is a single pin detection threshold.
And 8: if the received vector is detected as a single pin, then
Figure BDA0003026233140000088
The process of multiple iteration can be artificially set for L times of iteration, and meanwhile, when a single pin of the UE user number is found, the iteration is stopped. Finally, the estimated mapping
Figure BDA0003026233140000089
To the actual beam index
Figure BDA00030262331400000810
In summary, the present invention provides a novel millimeter wave multi-user beam alignment scheme, which can be applied to uplink multi-user beam alignment of an actual millimeter wave multi-antenna system. The scheme researches a wave beam alignment algorithm framework based on sparse coding, provides a novel sparse coding and decoding method aiming at a noise scene, and is based on the wave beam alignment framework, the performance is superior to the latest wave beam alignment algorithm, and the estimation channel performance approaches to the traditional algorithm based on compressed sensing under the full alignment condition.

Claims (1)

1. A novel millimeter wave multi-user beam alignment method, in a millimeter wave multi-user system, comprises a base station BS and K user UEs, wherein the BS end is provided with NRA receiving antenna and NRFA radio frequency link, NRF<NRAnd the kth UE is equipped with MTAn antenna and MRFA radio frequency link, wherein the beam alignment method comprises the steps of:
s1, the BS end receives a plurality of UE transmitting beams simultaneously and passes through an RF integration matrix
Figure FDA0003026233130000011
And a digital integration matrix
Figure FDA0003026233130000012
The locally customized beamforming codebook W (t) ═ WRF(t)WBB(t)＝FBSv (t), where v (t) represents an index matrix of quantization angles, where the non-zero values are 1, FBSRepresenting a DFT matrix; the BS side receives data by using different RF links, and the receiving side signals are represented as:
Figure FDA0003026233130000013
wherein
Figure FDA0003026233130000014
And K respectively represents the RF precoding matrix, the digital precoding matrix and the number of UE in the uplink channel,
Figure FDA0003026233130000015
is a beam space representation method in which
Figure FDA0003026233130000016
And
Figure FDA0003026233130000017
denotes a DFT matrix, s (t) is a transmission signal, N (t) -CN (0,1) denotes an additive noise vector of Gaussian distribution;
each RF link is processed individually by the receiving end at a time, and the data at the receiving end is represented as:
Figure FDA0003026233130000018
wherein the content of the first and second substances,
Figure FDA0003026233130000019
indicating selection
Figure FDA00030262331300000110
One of the rows in the group (a),
Figure FDA00030262331300000111
representing a virtual angular domain index, fk(t) for the transmission vectors of k users, for the BS, periodically scanning the receiving end beam space by simultaneously forming a plurality of beams;
s2, UE transmits a plurality of wave beams simultaneously, and the transmission vector is fk(t)＝FRF,k(t)FBB,k(t)＝FMSψk(t) in which
Figure FDA00030262331300000112
Coding matrix for representing k-th user, and reducing received data to riR, expressed as:
Figure FDA00030262331300000113
wherein
Figure FDA0003026233130000021
S3, collecting data at time T:
Figure FDA0003026233130000022
s4, defining T as MN, designing a measurement matrix
Figure FDA0003026233130000023
Divide it into two parts, including sparse coding matrix
Figure FDA0003026233130000024
And a detection matrix
Figure FDA0003026233130000025
The measurement matrix psi is:
ψ＝G⊙S
wherein |, indicates a line tensor operation, re-indicating the measurement matrix ψ as:
Figure FDA0003026233130000026
wherein G isiAnd SiRespectively represent the ith columns of matrix G and matrix S, an
Figure FDA0003026233130000027
Represents the Kronecker product;
s5, constructing a sparse coding matrix
Figure FDA0003026233130000028
Suppose a bipartite graph
Figure FDA0003026233130000029
In the set, the m-th detection node is divided into d stages, wherein each left node is randomly connected with one in each stageA right node, defining a set F ═ F1…fdRepresents the number of right nodes at the stage i as fiAnd, for all i and random redundancy parameters μ, fiμ K + o (1); constructing a sparse coding matrix based on a bipartite graph, so that each phase has a circularly translated sub-sampling graph;
s6, aiming at noise scenes, designing a sparse detection matrix
Figure FDA00030262331300000210
Wherein each phase has a column of values represented as
Figure FDA00030262331300000211
Wherein M isiThe number of non-zero elements in the matrix G in each layer is counted; matrix DiThe medium element is a random gaussian variable and remains constant modulus; transmitting beams through the constructed sparse coding matrix and the constructed sparse detection matrix;
s7, detecting whether the received vector is a zero pin, wherein the definition of the zero pin is that when a right node is not connected to the virtual angle domain channel
Figure FDA00030262331300000212
Is a zero pin:
Figure FDA00030262331300000213
wherein
Figure FDA00030262331300000214
Which is indicative of the minimum signal power,
Figure FDA00030262331300000215
is the minimum noise power, ε1Is zero pin detection threshold, ri,j[1]Correspondingly diluting a received first numerical value of a j pin vector at the ith stage in the coding matrix;
s8, if yesIf the received vector is not zero-lead, then the received lead vector is assumed to be single-lead and its beam index pair is estimated simultaneously
Figure FDA0003026233130000031
The definition of single pin is that when a right node has and only communicates with the angle domain
Figure FDA0003026233130000032
When one non-zero element is connected, the non-zero element is a single pin, and for the ith pin of each layer, the most possible coefficients are obtained by using a maximum likelihood algorithm as follows:
Figure FDA0003026233130000033
estimated of
Figure FDA0003026233130000034
Expressed as the minimum value of the following parameters
Figure FDA0003026233130000035
S9, using known checking steps to decide whether the received vector is a single pin, the following decision criteria are used:
Figure FDA0003026233130000036
wherein
Figure FDA0003026233130000037
Which is indicative of the minimum signal power,
Figure FDA0003026233130000038
is the minimum noise power, ε2Detecting a threshold for a single pin;
S10、if the received vector is detected as a single pin, then
Figure FDA0003026233130000039
Iterating the process for multiple times until obtaining a single pin of the UE user number or reaching the upper limit of the iteration times, stopping iteration, and finally mapping the estimated
Figure FDA00030262331300000310
To the actual beam index
Figure FDA00030262331300000311
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